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  pdftitle={Bayesian data analysis},
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  pdfauthor={Aki Vehtari},
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\section*{Bayesian data analysis -- reading instructions 12} 
\smallskip
{\bf Aki Vehtari}
\smallskip

\subsection*{Chapter 12}

Outline of the chapter 12
\begin{list}{$\bullet$}{\parsep=0pt\itemsep=2pt}
\item 12.1 Efficient Gibbs samplers (not part of the course)
\item 12.2 Efficient Metropolis jump rules (not part of the course)
\item 12.3 Further exetensions to Gibbs and Metropolis (not part of the course)
\item 12.4 Hamiltonian Monte Carlo (used in Stan)
\item 12.5 Hamiltonian dynamics for a simple hierarchical model (read through)
\item 12.6 Stan: developing a computing environment (read through)
\end{list}

\noindent
Python/R Stan demos
\begin{list}{$\bullet$}{\parsep=0pt\itemsep=2pt}
\item See rstan\_demo.Rmd, pystan\_demo.py, pystan\_demo.ipynb
  for demos how to use Stan from R/Python and several model examples
\end{list}

\noindent
There is only 8 pages to read (sections 12.4-12.6) what is inside Stan.

\subsection*{MCMC animations}

These don't include the specific version of dynamic HMC in Stan, but are useful illustrations anyway.
 \begin{itemize}
 \item Markov Chains: Why Walk When You Can Flow? \url{http://elevanth.org/blog/2017/11/28/build-a-better-markov-chain/}
 \item MCMC animation site by Chi Feng \url{https://chi-feng.github.io/mcmc-demo/}
 \end{itemize}


\subsection*{Hamiltonian Monte Carlo}

An excellent review of static HMC (the number of steps in dynamic
simulation are not adaptively selected) is
\begin{itemize}
\item Radford Neal (2011). MCMC using Hamiltonian dynamics. In Brooks
  et al (ed), {\em Handbook of Markov Chain Monte Carlo}, Chapman \&
  Hall / CRC Press. Preprint \url{https://arxiv.org/pdf/1206.1901.pdf}.
\end{itemize}

Stan uses a variant of dynamic Hamiltonian Monte Carlo (using adaptive
number of steps in the dynamic simulation), which has been further
developed since BDA3 was published. The first dynamic HMC variant was
\begin{itemize}
\item Matthew D. Hoffman, Andrew Gelman (2014). The No-U-Turn Sampler:
  Adaptively Setting Path Lengths in Hamiltonian Monte Carlo. {\em
    JMLR},
  15:1593--1623 \url{http://jmlr.org/papers/v15/hoffman14a.html}.
\end{itemize}
The No-U-Turn Sampler gave the name NUTS which you can see often
associated with Stan, but the current dynamic HMC variant implemented
in Stan has some further developments described (mostly) in
\begin{itemize}
\item Michael Betancourt (2018). A Conceptual Introduction to
  Hamiltonian Monte Carlo. arXiv preprint arXiv:1701.02434
  \url{https://arxiv.org/abs/1701.02434}.
\end{itemize}

Instead of reading all above, you can also watch a nice introduction
video
\begin{itemize}
\item Scalable Bayesian Inference with Hamiltonian Monte Carlo by
  Michael Betancourt
  \url{https://www.youtube.com/watch?v=jUSZboSq1zg}
\end{itemize}

\subsection*{Divergences and BFMI}

Divergences and Bayesian Fraction of Missing Information (BFMI) are
HMC specific convergence diagnostics developed by Michael Betancourt
after BDA3 was published.

\begin{itemize}
\item Divergence diagnostic checks whether the discretized dynamic
simulation has problems due to fast varying density. See more in a
case study
\url{http://mc-stan.org/users/documentation/case-studies/divergences_and_bias.html.}
\item BFMI checks whether momentum resampling in HMC is sufficiently efficient. See more in
\url{https://arxiv.org/abs/1604.00695}
\item Brief Guide to Stan's Warnings
\url{https://mc-stan.org/misc/warnings.html} provides summary of
available convergence diagnostics in Stan and how to interpret them.
\end{itemize}
\subsection*{Further information about Stan}

\begin{itemize}
\item \url{http://mc-stan.org/} \& \url{http://mc-stan.org/documentation/}
  \begin{itemize}
  \item I recommend to start with these
    \begin{itemize}
    \item Bob Carpenter, Andrew Gelman, Matt Hoffman, Daniel Lee, Ben
      Goodrich, Michael Betancourt, Marcus A. Brubaker, Jiqiang Guo,
      Peter Li, and Allen Riddell (2015) In press for Journal of
      Statistical Software. Stan: A Probabilistic Programming
      Language. \url{http://www.stat.columbia.edu/~gelman/research/published/stan-paper-revision-feb2015.pdf}
    \item Andrew Gelman, Daniel Lee, and Jiqiang Guo (2015) Stan: A
      probabilistic programming language for Bayesian inference and
      optimization. In press, Journal of Educational and Behavior
      Science. \url{http://www.stat.columbia.edu/~gelman/research/published/stan_jebs_2.pdf}
    \end{itemize}
  \item Basics of Bayesian inference and Stan, parts 1+2 Jonah Gabry \& Lauren Kennedy \url{https://www.youtube.com/playlist?list=PLuwyh42iHquU4hUBQs20hkBsKSMrp6H0J}
  \item Modeling Language User's Guide and Reference Manual (more complete reference with lot's of examples) \url{https://github.com/stan-dev/stan/releases/download/v2.17.0/stan-reference-2.17.0.pdf}
  \end{itemize}
\end{itemize}

\end{document}

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